An Application of the Level Set Method to Underwater Acoustic Propagation (Communications in Computational Physics, 2012)
An algorithm for computing wavefronts, based on the high frequency approximation to the wave equation, is presented. This technique applies the level setmethod to underwater acoustic wavefront propagation in the time domain. The levelset method allows for computation of the acoustic phase function using establishednumerical techniques to solve a first order transport equation to a desired order of accuracy. Traditional methods for solving the eikonal equation directly on a fixed gridlimit one to only the first arrivals, so these approaches are not useful when multi-pathpropagation is present. Applying the level set model to the problem allows for thetime domain computation of the phase function on a fixed grid, without having to restrict to first arrival times. The implementation presented has no restrictions on rangedependence or direction of travel, and offers improved efficiency over solving the fullwave equation which under the high frequency assumption requires a large numberof grid points to resolve the highly oscillatory solutions. Boundary conditions are discussed, and an approach is suggested for producing good results in the presence ofboundary reflections. An efficient method to compute the amplitude from the level setmethod solutions is also presented. Comparisons to analytical solutions are presentedwhere available, and numerical results are validated by comparing results with exactsolutions where available, a full wave equation solver, and with wavefronts extractedfrom ray tracing software.